I've owned basses that have had the facility to be strung through both positions (bridge rear/thru-body) and I have to say that there was no discernible difference to my ear; whether in isolation or with a full band cranked. In fact I had grief with one bass when thru-body stringing and the windings came to the saddle point and if using flats the string would 'fracture' (for want of a better word), due to the break angle coming over the saddles from the rear (fnarr). However, it works for some so go with what you feel is best... your ears may be in better shape than mine.